Identification Via Quantum Channels
Andreas Winter
TL;DR
This work surveys identification via quantum channels, extending Ahlswede and Dueck's identification theory to the quantum regime and distinguishing multiple identification notions and capacities. It develops a decoupling-based framework (weak decoupling duality) that links quantum ID-capacities to environment forgetfulness, yielding single-letter, additive formulas in key cases and clarifying the role of amortization. The results show that quantum identification can outperform classical transmission capacities and can bound classical ID-capacities via fingerprinting, with concrete bounds for channels like the erasure channel. The paper also outlines a rich set of open problems, including whether the simultaneous and non-simultaneous ID-capacities coincide in general and how amortization shapes the landscape of quantum and classical ID capacities. Overall, the framework provides deep connections between identification, decoupling, and entanglement-assisted capacities, and points to substantial future work in quantum identification theory.
Abstract
We review the development of the quantum version of Ahlswede and Dueck's theory of identification via channels. As is often the case in quantum probability, there is not just one but several quantizations: we know at least two different concepts of identification of classical information via quantum channels, and three different identification capacities for quantum information. In the present summary overview we concentrate on conceptual points and open problems, referring the reader to the small set of original articles for details.